ITA | ENG
B010504 - ADVANCED REAL ANALYSIS
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Type of Assessment
Course program
Academic Year 2017-18
Course year
First year - First Semester
Belonging Department
Information Engineering (DINFO)
Course Type
Single education field course
Scientific Area
MAT/05 - MATHEMATICAL ANALYSIS
Credits
6
Teaching Hours
48
Teaching Term
18/09/2017 ⇒ 22/12/2017
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Teaching Language
Italian
Course Content
Elements of Probability Theory and Stochastic processes. An introduction to measure theory. Statistics.
Suggested readings (Search our library's catalogue)
Laura Poggiolini Note di Calcolo delle Probabilità. Pitagora Editrice.
Notes to be doenloaded from the web (will be made available during the course)
Notes to be doenloaded from the web (will be made available during the course)
Learning Objectives
Introduction to methods and results of probability and statistics
Prerequisites
Topics from the courses Analisi Matematica I e II, Geometria e Algebra lineare
Teaching Methods
Classes
Type of Assessment
The exam is divided:
in a written part whose objective is the capability of applying the topics of the course to simple examples e the knowledge of the main results of the subject;
in an oral part whose obective is to verify the theoretical knowledge of the topics of the course
in a written part whose objective is the capability of applying the topics of the course to simple examples e the knowledge of the main results of the subject;
in an oral part whose obective is to verify the theoretical knowledge of the topics of the course
Course program
Elements of probability theory: probability spaces, random variables, expected value, variance, moments. Some examples of random variables: binomial, Poisson, Gaussian r.v. Conditional probability, Bayes theorem, independence of events and of random variables. Conditional expectation. Markov and Chebychev inequalities. Large number theorems, Central Limit Theorem.
Measure theory: Lebesgue measure, Lebesgue integral. abstract measures and probability measures. An introduction to stochastic processes: covariance and correlation. Martingales and Brownian motion.
Topics from statistics: sampling, confidence intervals, Statistical hypothesis testing, consistent estimators, non-bias estimators. Estimators of sample mean and sample variance. Student's t distribution, chi-square distribution, Pearson's chi-squared test. Regression, maximal likelihood.
Measure theory: Lebesgue measure, Lebesgue integral. abstract measures and probability measures. An introduction to stochastic processes: covariance and correlation. Martingales and Brownian motion.
Topics from statistics: sampling, confidence intervals, Statistical hypothesis testing, consistent estimators, non-bias estimators. Estimators of sample mean and sample variance. Student's t distribution, chi-square distribution, Pearson's chi-squared test. Regression, maximal likelihood.